Calibration Of Safety Factors Research Articles

Partial safety factor calibration using surrogate models: An application for running safety of ballasted high-speed railway bridges

Traditionally, regulations employ semi-probabilistic methods with partial safety factors to control design limits. Calibrating these partial safety factors involves estimating the target reliability level and optimizing the partial safety factor values in order to minimize the deviation of the safety index between the considered design scenarios and the target value. This procedure necessitates performing a demanding amount of reliability analyses and is often carried out for simplified design situations. Therefore, high computational costs must be accepted for design problems formulated with complex computational models. This study implements a meta-modeling approach based on active learning in the partial safety calibration procedure, enabling its application to computationally intensive problems. Subsequently, the approach is applied to the running safety of ballasted high-speed railway bridges. This limit state implicitly accounts for the phenomenon of ballast destabilization, the occurrence of which disturbs the load path from the rail level to the bridge structure. The dramatic increase in train operating speeds in recent decades has increased the possibility of this design limit state being violated due to resonance. Despite the evident safety concerns, the adopted safety factors appear to be solely based on engineering judgments rather than calibration through higher-level reliability analysis. Therefore, the proposed calibration method is employed to determine the corresponding partial safety factors for various maximum allowable operating train speeds. The newly calibrated partial safety factors allow for a permissible maximum vertical acceleration of the bridge deck approximately 25% higher than the conventional design approaches. Therefore, incorporating these factors into the design procedure may lead to the construction of lighter bridges.

Uncertainty analysis of extreme mooring loads associated with environmental contours and peak tension distributions

This paper aims to assess the uncertainty on the extreme mooring loads of floating system considering short-term variability. Two environmental contour approaches based on the inverse First and Second Order Reliability Methods are employed to identify critical sea states that may give rise to extreme loads. The uncertainty related to the construction of environmental contours is addressed including significant differences due to marginal distribution fitting, parameter estimation methods and joint models. Three measured datasets are analysed using a known conditional joint distribution and proposed mixed copula model. 3-h time domain numerical simulation for each sea state is conducted and the characteristic extreme responses of mooring lines subjected to design loads are assessed. The uncertainties due to various statistical models including the average conditional exceedance rate method as well as global maxima, peak-over-threshold method combined with Gumbel distribution, Generalized Extreme Value distribution, Generalized Pareto distribution and 3-parameter Weibull distribution are investigated and quantified. It is observed that marginal distributions, joint models and parameters estimation methods have apparent effect on design loads estimation, and the extreme tensions of the semi-submersible platform shows significant difference using various probabilistic models. The results indicate that those epistemic uncertainties should be account for in the reliability analysis or safety factor calibration for mooring systems.

Calibration of safety factors for prestressed stayed steel columns

Previous studies have investigated the behaviour of prestressed stayed steel columns with a view to developing design guidelines. As most of the modern standards move towards calibrated safety factors, there is a need to explore the design expectations of these structures from a probabilistic perspective. This has not been studied in the literature till now, perhaps due to lack of clarity on underlying uncertainties, failure models and reliability levels. In this paper, the relevant reliability levels were studied to highlight the critical modes for such structures. A sensitivity analysis was performed on the random variables to investigate their impact on the model output. The reliability levels found through appropriate analysis were then compared with target reliabilities to calibrate partial safety factors to be used in the design of these structures. A range of safety factor values were found depending on the conditions adopted in the calibration and target reliability studies.

Statistical data expansion using Kriging for probabilistic capacity factor calibration

This study proposes a new reliability-based capacity factor calibration method based on the EN 1990 Annex D method in combination with Kriging for a statistical data expansion. The original EN 1990 Annex D method has been widely used in partial safety factor or capacity factor calibrations in international structural design standards by rigorously considering the modelling error of the design equations in comparison with real experimental data. However, as the number of experimental data is often limited in practical situations, large statistical uncertainty needs to be incorporated in the safety factor calibration process, and the calibrated partial safety factors or capacity factors have large variations. In the proposed method, Kriging, a data-driven nonlinear interpolation method, is utilised to statistically expand the experimental database used for modelling error estimation when experimental data are limited. To make the calculation rigorous, the Kriging error of the statistically expanded data is also estimated and incorporated into the proposed framework. The proposed method is demonstrated through two numerical examples and three real world structural design examples including the shear strength of reinforced concrete beams and the axial resistance of concrete-filled steel tubular stub columns with circular and rectangular sections, each of which has more than 300 experimental data for verification. The results show that the proposed method always improves the calibration results by statistical data expansion, which does not need any additional physical costs for experiments.

Calibration of safety factors for offshore wind turbine support structures using fully coupled simulations

The offshore wind industry experienced a boost during the last decade in terms of size of wind farms and rated capacity of the wind turbines: towers are getting taller and blades are getting longer, constantly facing new and complex challenges. Because of the relative immaturity of the wind industry, and the fact that the offshore design standards stemmed from the oil and gas industry, it is generally acknowledged that the reliability levels achieved, although not very well understood, might result in partial safety factors not optimal for OWT. This paper addresses this situation by studying the reliability levels delivered by the current standards and assessing the validity of the safety factors through a reliability-based code calibration. The combination of the low probability of failure imposed on the design of OWTs and the computational cost of the aero-elastic time-domain simulations brings out the need to develop new approaches for reliability analyses. In this paper, the reliability analysis is performed using a Kriging surrogate model to approximate the load-effect from the aero-elastic simulations converting expensive-to-evaluate limit state functions to explicit functions. Subsequently, a calibration of the safety factors is carried out using the probabilistic models from literature. The approach is applied to an industry-reference turbine and support structure. The results showed very low probabilities of failure for the most severe design cases and confirm that the safety factors from the IEC are mostly adequate.

Safety factor calibration for a new model of shear strength of reinforced concrete building beams and slabs

When assessing existing structures, the availability of adequate safety factors, calibrated with the most accurate models, and for established target reliability indexes, is of critical importance in order to take the right decision regarding the maintenance/repair/strengthening interventions. In the case of shear resistance in reinforced concrete (RC) structures, when using the current design codes provisions for new constructions in assessment results that, in many cases, existing structures may be considered unsafe, implying large economic costs in strengthening or even dismantling. In this research, a proposal of safety factor relative to a recently developed model for shear strength, for elements with and without transversal reinforcement, based on a reliability-based calibration is presented. A formulation is proposed to determine the adequate strength factor for a selected target reliability index of the existing structure and desired remaining service life by means of a safety factor format, considering the load factors present in the Eurocodes. The calibration is carried out considering typical geometry and load ratios of building floors, as well as normal and high strength concrete. The derived safety factor is almost independent of the chosen remaining service life.

Lazy-Wave Buoyancy Length Reduction Based on Fatigue Reliability Analysis

The current downturn of the oil and gas industry force managers to take hard decisions about the continuity of projects, resulting in delays, postponements, or even their cancellation. In order to keep with them, the rush for cost reduction is a reality and the industry is pushing the involved parties to be aligned with this objective. The Brazilian presalt region, characterized by ultra-deep waters, faces this scenario where flexible risers in lazy-wave configurations are usually adopted as a solution to safe transfer fluids from sea bed until the floating unit. The smaller the buoyancy length, the cheaper the project becomes, reducing the necessary amount of buoys and the time spent for its installation. This paper investigates the possibility of buoyancy length reduction of lazy-wave configurations by using structural reliability methods on fatigue failure mode. The application of the fatigue reliability approach considers four 6 in flexible riser configurations: an original lazy-wave, a lazy-wave with less 30% of buoyancy length, another one with less 50% of buoyancy length and a free-hanging. Failure probabilities and safety factor calibration curves are shown for each configuration and compared among themselves. The results indicate the possibility of defining a lazy-wave configuration with smaller buoyancy lengths, reaching 75% of reduction without changing the preconized high safety class. Structural reliability analysis is available to help engineers understand the driving random variables of the problem, supporting the actual scenario of cost reduction for better decision-making based on quantified risk.

Mathematical models for prediction of safety factors for a simply supported steel beam

The reliability-based calibration of safety factors for the design of a simply supported steel beam, based on BS5950 (2000) is presented in this research work. The calibration was undertaken using a specialized computer program in Microsoft excel environment developed by the Joint Committee for Structural Safety (JCSS) CODE-CAL 2001. The design variables considered were modeled using the software, and the safety factors for the material, dead and live load were calibrated by varying the safety index. From the results obtained, mathematical prediction models were developed using a least square regression analysis for bending, shear and deflection modes of failure considered in the study. The results showed that the safety factors for material, dead and live load are not unique, but they are influenced by safety index and it was also shown that the safety factors for material, dead and live load vary from 0.61 to 1.15, 1.44 to 1.91 and 1.40 to 1.65 respectively for both bending and shear modes of failure. For deflection mode of failure, the results showed that the safety factors for material, dead and live load vary from 1.08 to 1.56, 1.10 to 1.17 and 0.83 to 1.25 respectively for target safety index (βt) of 2.0 to 4.5. The mathematical prediction models developed for both bending and shear modes of failure are the same. Therefore, it is recommended that the mathematical prediction models developed in this study for bending and deflection modes of failure could be used when designing a simply supported steel beam to BS 5950 (2000).Keywords: reliability, code calibration, load factor, safety factor, design, steel beam

Reliability Based Design of RC Beams With Recycled Aggregate and Steel Fibres

This study proposes a reliability analysis framework for the design of secondary beams fabricated with steel fibre reinforced recycled aggregate concrete (SFRRAC). The use of SFRRAC in fabrication of structural members is proposed due to its optimal combination of recycled aggregate concrete (RAC) and steel fibre (SF), to gain advantages in terms of environmental effects, production costs, and structural properties. However, structural members composed of new materials should be used for practical structural design according to proper design equations and safety factors determined via test-aided reliability analysis. The current international provisions are applicable only to natural aggregate concrete (NAC) beams, and cannot be directly applied to SFRRAC beams. This study adopts a safety factor calibration method based on the first-order reliability method (FORM) to evaluate the relation between the safety factor and the target reliability level for SFRRAC beams designed using the existing models for RC beams provided in Australian, American, and European design codes. This evaluation is based on the proposed improved prediction model for the flexural capacity of RAC due to the addition of SF. Furthermore, the optimal contents of SF in SFRRAC beams with 100% recycled aggregates (RA) to make the beams equivalent to NAC beams, in terms of moment carrying capacity are estimated using a proposed inverse analysis. The optimal contents are estimated to be around 0.015% of SF (by volume).

Reliability based calibration of safety factors for unstiffened cylindrical composite shells

The feasibility of probabilistic design methods to overcome conservatism associated with deterministic design methods for unstiffened cylindrical composite shells has been shown, but studies are frequently based on assumptions regarding relevant uncertainties due to the lack of available data. The reliability based calibration method suggested here relies on extensive measurements regarding the statistical characteristics of thickness, fibre volume fraction, fibre orientation, material stiffness and geometric imperfections of 11 previously tested cylinders. Furthermore, the stiffness of the potting of tested cylinders is estimated using Finite Element Analysis and the introduction of a pre-stress state through the potting process investigated. Following a sensitivity study, Bayesian inference is used to update the information of relevant uncertain variables. Monte Carlo simulation is employed to compute the distribution functions of the buckling load, and these are used to calibrate structural safety factors at a chosen reliability level. A multiplicative error model is established to compute safety factors covering the model uncertainty inherent to the approach. In combining these two safety factors in a Bayesian sense, a transparent, updatable safety-factor concept is developed, leading to less conservative design loads than currently considered.

Reliability of masonry walls subjected to in‐plane loading: A slip failure along head joints / Zuverlässigkeit von Mauerwerkswänden bei Belastung in der Ebene: Versagen entlang der Stoßfugenflucht

AbstractMasonry structures are a sustainable, economical and traditionally widely used type of construction. However, current masonry design codes are rather conservative, so there is a growing need for revision i.e. calibration of safety factors to improve the allocation of material resources. In this paper, we investigate the probability of occurrence of slip failure along head joints (perpends) in masonry subjected to in‐plane loading. An appropriate limit state function is established and the masonry material properties and loads are defined as random variables in order to simulate likelihood of occurrence of a slip failure regime along the head joints. Furthermore, an example of masonry wall with probabilistic analysis outcomes using Monte Carlo simulation is presented and recommendations for further work are provided.

Test-Based Calibration of Safety Factors for Capacity Models

AbstractA simple procedure to calibrate the safety factor of capacity models is presented. The calibration can be carried out based on any available database of experimental tests, even of limited size. The procedure aims to assess the model capability of predicting the test results and to calibrate the safety factor so that the capacity equation meets the target reliability level required by the code or sought by the calibrator. After predicting each test of the database with the capacity equation under consideration, the test-prediction pairs are checked for the property of linearity, and the relative error for the properties of homoscedasticity and normality. Once these properties are fulfilled—which may require a nonlinear transformation of the test values and/or the predictions—the closed-form equation proposed in this paper is employed to compute a target design value. The model safety factor is finally obtained by comparing such target design value with the design value obtained from the code. The ...

Partial safety factor calibration from stochastic finite element computation of welded joint with random geometries

Welded joints are used in various structures and infrastructures like bridges, ships and offshore structures, and are submitted to cyclic stresses. Their fatigue behaviour is an industrial key issue to deal with and still offers original research subjects. One of the available methods relies on the computing of the stress concentration factor. Even if some studies were previously driven to evaluate this factor onto some cases of welded structures, the shape of the weld joint is generally idealized through a deterministic parametric geometry. Previous experimental works however have shown that this shape plays a key role in the lifetime assessment. We propose in this paper a methodology for computing the stress concentration factor in presence of random geometries of welded joints. In view to make the results available by engineers, this method merges stochastic computation and semi-probabilistic analysis by computing partial safety factors with a dedicated method.

Identification of the Uncertainties for the Calibration of the Partial Safety Factors for Load in Tidal Turbines

Tidal energy is nowadays one of the fastest growing types of marine renewable energy. In particular, Horizontal Axis Tidal Turbines (HATTs) are the most advanced designs and the most appropriate for standardization. This paper presents a review of actual design criteria focusing on the identification of the uncertainties that technology developers need to address during the design process. Key environmental parameters like turbine inflow conditions or predictions of extreme values are still grey areas due to the lack of site measurements and the uncertainty in metocean model predictions. A comparison of turbulence intensity characterization using different tools and at different points in time shows the uncertainty in the prediction of this parameter. Numerical models of HATTs are still quite uncertain, often dependent on experience of the people running them. In the reliability-based calibration of partial safety factors, the uncertainties need to be reflected on the limit state formulation. This paper analyses the different types of uncertainties present in the limit state equation. These uncertainties are assessed in terms of stochastic variables in the limit state equation. In some cases, advantage can be taken from the experience from offshore wind and oil and gas industries. Tidal turbines have a mixture of the uncertainties present in both industries with regard to partial safety factor calibration.

Statistical calibration of safety factors for flexural stiffness of composite columns

Composite column design is strongly influenced by the computation of the critical buckling load, which is very sensitive to the effective flexural stiffness (EI) of the column. Because of this, the behaviour of a composite column under lateral loading and its response to deflection is largely determined by the EI of the member. Thus, prediction models used for composite member design should accurately mirror this behaviour. However, EI varies due to several design parameters, and the implementation of high-strength materials, which are not considered by the current composite design codes of practice. The reliability of the design methods from six codes of practice (i.e., AS 5100, AS/NZS 2327, Eurocode 4, AISC 2010, ACI 318, and AIJ) for composite columns is studied in this paper. Also, the reliability of these codes of practice against a serviceability limit state criterion are estimated based on the combined use of the test-based statistical procedure proposed by Johnson and Huang (1997) and Monte Carlo simulations. The composite columns database includes 100 tests of circular concrete-filled tubes, rectangular concrete-filled tubes, and concrete-encased steel composite columns. A summary of the reliability analysis procedure and the evaluated reliability indices are provided. The reasons for the reliability analysis results are discussed to provide useful insight and supporting information for a possible revision of available codes of practice.

Safety factor calibration for bridge concrete girders

Safety factors proposed in codes CEB, B.A.E.L 91 and EUROCODE 1 cover a great number of uncertainties; making them inadequate for the assessment of existing structures. Suitable safety factors are established using a probabilistic assessment, once real dimensions, materials strength and existing structures deterioration mechanisms are taken into account. This paper presents a calibration method for safety factors using a typical set of RC bridges in France. It considers the principal stages of corrosion provoked by <TEX>$CO_2$</TEX> and <TEX>$Cl^-$</TEX> penetration and threshold indexes (<TEX>${\beta}_0$</TEX>) for existing structures. Reliability indexes are determined by the FORM method in the calibration method.

Reliability Acceptance Criteria for Deteriorating Elements of Structural Systems

A systematic approach to determining reliability-based acceptance criteria for deteriorating elements in structural systems is proposed as a basis for calibration of safety factors in codes and standards and for verifying acceptability of inspection and maintenance strategies for specific structures. The goal is to establish deterioration acceptance criteria for the elements of a structural system in compliance with criteria formulated for the system. Existing methods significantly overestimate the deterioration reliability of redundant structural systems because they neglect the joint effect of deterioration failures of different elements. To more realistically capture the load-sharing behavior of deteriorating redundant structural systems, it is proposed to establish deterioration acceptance criteria on the basis of easily computable, idealized structural systems, which are calibrated to the characteristics of the real structure. The approach is validated on an example structural system and is found to represent a significant improvement over current methods. The paper concludes with a study of the main factors influencing acceptance criteria of deterioration reliability.

Reliability-based comparative study for mooring lines design criteria

The characteristic environmental load effect for the design of mooring systems of floating units can be defined by means of three procedures: (a) the one associated to an extreme sea state with a given return period, (b) the worst one from a set of sea states on a contour line associated to a return period or (c) the extreme one based on response statistics for a long-term period. This work presents the result of a reliability-based partial safety factor calibration study for a LRFD mooring line design criteria considering the three approaches mentioned above. The calibration exercise is applied to three FPSOs considering North Sea environmental conditions and different water depths: 200, 800 and 3000 m. The mooring systems investigated take into account mooring lines made up of chains and polyester ropes. It is shown that, among all cases investigated, the design procedure based on the long-term response is the one that presents less scattered reliability indices around the target level.

Limit equilibrium conditions for deep sea sediments and infinite plane failure analysis, offshore Gabon

Deep offshore geological surveys have been conducted on the Gabon continental shelf. A geological description of the area explored reveals the presence of seepage features and gas bubbles in the upper 50 m of sediments. Seafloor instabilities also occurred at quite low slope gradients. A laboratory study of the mechanical behavior of the sampled sediments helped verify that the ratio between undrained shear strength and preconsolidation pressure is very high at low confining pressures in terms of classical empirical regressions used mostly by geotechnicians. These experiments also lead to a mathematical model of undrained shear strength versus depth profile for some saturated and normally consolidated sediments. Hypotheses are developed concerning the undrained behavior of underconsolidated sediments. The eventuality of seepage forces in sediments leads to the calibration of safety factors under drained and undrained conditions. It is established that static infinite plane failure cannot be triggered at low slopes if the sediments are normally consolidated. Graphs are finally constructed in order to visualize the impact of water excess pore pressure on superficial sediments stability. A realistic physical interpretation is also given.